While a mansion tax could play a part in solving these problems, it isn't enough. As the mayoral election approaches, the real question on Londoners' lips should be: what will the next London mayor do to tackle London's housing crisis?

Yet from May, the next mayor will have significant new powers over housing in the capital, handing the winning candidate a golden opportunity to fix London's housing and make a real difference to Londoners' lives. This includes, for the first time, control over the budget for building new housing, which means the buck will stop with the mayor when it comes to delivering more affordable homes.

So far, no mayor has managed to build anything close to the 33,400 homes the capital needs each year to meet demand. The next mayor will not only control the money, but will also take ownership of a large chunk of the capital's public land on which many of these homes could be built.

The next mayor should also start getting a grip on London's rental market, which now houses one in four Londoners. A quality lettings service backed by the mayor could reduce the misery and uncertainty of setting up a new tenancy – including hefty deposits that can mean upfront costs of up to £2,000 per move. A dedicated team to tackle rogue landlords in the capital would also help to give tenants the protection they need.

Once they're in a home, London's 200,000 private renting families – a quarter of all families in the capital – would also welcome a deal that enabled them to stay in that home for the long term, to put down roots and see their kids through school. That means having a degree of certainty in their tenancy, and predictability about future rent rises. London is one of the few capitals in Europe without this.

An ambitious mayor should not stop there. If some form of mansion tax does go ahead, it's vital that the next mayor demands that some of the proceeds from the new tax are ring-fenced for new housing in the capital. They should also look for ways to leverage the power of London's financial sector to find new sources of private investment for the homes that London needs. The government has already launched its own review on the barriers to greater institutional investment in the private rental market. The mayor could play a much greater role in encouraging the investment industry, including pension funds, to invest more in residential development in the capital.

Come 4 May, the next London mayor will have a historic opportunity to fix London's housing crisis. Londoners should be asking the candidates whether or not they will take it.